Example 4.7.2.11 (Successor Cardinals). Let $\kappa $ be a cardinal. Proposition 4.7.2.8 implies that there exists another cardinal $\lambda $ such that $\kappa < \lambda $. By virtue of Remark 4.7.2.9, there is a smallest cardinal with this property. We denote this cardinal by $\kappa ^{+}$ and refer to it as the successor of $\kappa $.
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